A family of solutions to the Einstein-Maxwell system of equations describing relativistic charged fluid spheres

TL;DR

This paper develops a formalism to generate and analyze a broad family of exact solutions for charged fluid spheres in general relativity, extending previous models and ensuring their physical viability.

Contribution

Introduces a recurrence relation-based formalism to produce a wide class of exact Einstein-Maxwell solutions for charged fluid spheres.

Findings

Contains previously known solutions as special cases

Provides closed-form solutions for specific parameter ranges

Analyzes physical viability of the new solutions

Abstract

In this paper, we present a formalism to generate a family of interior solutions to the Einstein-Maxwell system of equations for a spherically symmetric relativistic charged fluid sphere matched to the exterior Reissner-Nordstr\"om spacetime. By reducing the Einstein-Maxwell system to a recurrence relation with variable rational coefficients, we show that it is possible to obtain closed-form solutions for a specific range of the model parameters. A large class of solutions obtained previously are shown to be contained in our general class of solutions. We also analyze the physical viability of our new class of solutions.